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<div class="title">IMEXTimeStepper.py</div>  </div>
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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00010"></a>00010 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00011"></a>00011 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00014"></a>00014 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00015"></a>00015 <span class="comment">#</span>
<a name="l00016"></a>00016 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00017"></a>00017 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00018"></a>00018 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00019"></a>00019 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00020"></a>00020 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00021"></a>00021 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00022"></a>00022 <span class="comment"># SOFTWARE.</span>
<a name="l00023"></a>00023 <span class="comment">#</span>
<a name="l00024"></a>00024 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00025"></a>00025 <span class="comment"># Mountain View, CA</span>
<a name="l00026"></a>00026 <span class="comment">#</span>
<a name="l00027"></a>00027 
<a name="l00028"></a>00028 __docformat__ = <span class="stringliteral">&#39;restructuredtext&#39;</span>
<a name="l00029"></a>00029 <span class="keyword">from</span> scipy.sparse.linalg <span class="keyword">import</span> spsolve <span class="keyword">as</span> spsolve
<a name="l00030"></a>00030 <span class="keyword">from</span> utils.ProjOperators <span class="keyword">import</span> oned_inner
<a name="l00031"></a>00031 <span class="keyword">from</span> numpy <span class="keyword">import</span> zeros
<a name="l00032"></a>00032 
<a name="l00033"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html">00033</a> <span class="keyword">class </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html">IMEXTimeStepper</a>(object):
<a name="l00034"></a>00034 
<a name="l00035"></a>00035     <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00036"></a>00036 <span class="stringliteral">    Implicit Explicit time stepper as described in:</span>
<a name="l00037"></a>00037 <span class="stringliteral"></span>
<a name="l00038"></a>00038 <span class="stringliteral">        @article{PIDpaper,</span>
<a name="l00039"></a>00039 <span class="stringliteral">           author =  {Liming Feng, Vadim Linetsky},</span>
<a name="l00040"></a>00040 <span class="stringliteral">           title =   {Pricing Options in Jump-Diffusion Models: An Extrapolation Approach.},</span>
<a name="l00041"></a>00041 <span class="stringliteral">           journal = {Options Research},</span>
<a name="l00042"></a>00042 <span class="stringliteral">           volume =  2,</span>
<a name="l00043"></a>00043 <span class="stringliteral">           year =    2008,</span>
<a name="l00044"></a>00044 <span class="stringliteral">           pages =   {304-325},</span>
<a name="l00045"></a>00045 <span class="stringliteral">        }</span>
<a name="l00046"></a>00046 <span class="stringliteral"></span>
<a name="l00047"></a>00047 <span class="stringliteral"></span>
<a name="l00048"></a>00048 <span class="stringliteral">    The algorithm presented here differs to the one in the paper on the</span>
<a name="l00049"></a>00049 <span class="stringliteral">    way boundary conditions are treated. Boundary conditions are assumed</span>
<a name="l00050"></a>00050 <span class="stringliteral">    to be zero in the paper, here we handle time dependent boundary conditions.</span>
<a name="l00051"></a>00051 <span class="stringliteral">    &quot;&quot;&quot;</span>
<a name="l00052"></a>00052 
<a name="l00053"></a>00053     __slots__ = [
<a name="l00054"></a>00054         <span class="stringliteral">&#39;m_adaptive&#39;</span>,
<a name="l00055"></a>00055         <span class="stringliteral">&#39;m_dolog&#39;</span>,
<a name="l00056"></a>00056         <span class="stringliteral">&#39;m_ftime&#39;</span>,
<a name="l00057"></a>00057         <span class="stringliteral">&#39;m_ival&#39;</span>,
<a name="l00058"></a>00058         <span class="stringliteral">&#39;m_jump&#39;</span>,
<a name="l00059"></a>00059         <span class="stringliteral">&#39;m_tol&#39;</span>,
<a name="l00060"></a>00060         <span class="stringliteral">&#39;m_rbc&#39;</span>,
<a name="l00061"></a>00061         <span class="stringliteral">&#39;m_srbop&#39;</span>,
<a name="l00062"></a>00062         <span class="stringliteral">&#39;m_slbop&#39;</span>,
<a name="l00063"></a>00063         <span class="stringliteral">&#39;m_stiff&#39;</span>,
<a name="l00064"></a>00064         <span class="stringliteral">&#39;m_lbc&#39;</span>,
<a name="l00065"></a>00065         <span class="stringliteral">&#39;m_load&#39;</span>,
<a name="l00066"></a>00066         <span class="stringliteral">&#39;m_mass&#39;</span>,
<a name="l00067"></a>00067         <span class="stringliteral">&#39;m_mesh&#39;</span>,
<a name="l00068"></a>00068         <span class="stringliteral">&#39;m_method&#39;</span>,
<a name="l00069"></a>00069         <span class="stringliteral">&#39;m_mrbop&#39;</span>,
<a name="l00070"></a>00070         <span class="stringliteral">&#39;m_mlbop&#39;</span>,
<a name="l00071"></a>00071         <span class="stringliteral">&#39;m_numsteps&#39;</span>,
<a name="l00072"></a>00072         <span class="stringliteral">&#39;m_numstates&#39;</span>,
<a name="l00073"></a>00073         <span class="stringliteral">&#39;m_quads&#39;</span>,
<a name="l00074"></a>00074         <span class="stringliteral">&#39;m_sfunc&#39;</span>,
<a name="l00075"></a>00075         <span class="stringliteral">&#39;m_xl&#39;</span>,
<a name="l00076"></a>00076         <span class="stringliteral">&#39;m_xr&#39;</span>,
<a name="l00077"></a>00077         ]
<a name="l00078"></a>00078 
<a name="l00079"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a1561984957ce1a15bc41e83291c042a5">00079</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a1561984957ce1a15bc41e83291c042a5">__init__</a>(self):
<a name="l00080"></a>00080         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00081"></a>00081 <span class="stringliteral">        Implicit - Explicit time stepper.</span>
<a name="l00082"></a>00082 <span class="stringliteral"></span>
<a name="l00083"></a>00083 <span class="stringliteral">        Variables:</span>
<a name="l00084"></a>00084 <span class="stringliteral">            m_adaptive (bool) ~ use adaptive time steps?.</span>
<a name="l00085"></a>00085 <span class="stringliteral">            m_dolog (bool) ~ log results.</span>
<a name="l00086"></a>00086 <span class="stringliteral">            m_tol (float) ~ tolerance for adaptive steps.</span>
<a name="l00087"></a>00087 <span class="stringliteral">            m_mass ~ mass matrix.</span>
<a name="l00088"></a>00088 <span class="stringliteral">            m_stiff ~ full pde.</span>
<a name="l00089"></a>00089 <span class="stringliteral">            m_jump ~ convolution.</span>
<a name="l00090"></a>00090 <span class="stringliteral">            m_lbc ~ left boundary condition ( function (x, t) )</span>
<a name="l00091"></a>00091 <span class="stringliteral">            m_lbop ~ pde compensation for implicit solution.</span>
<a name="l00092"></a>00092 <span class="stringliteral">            m_method ~ Euler, midpoint, extrapolation.</span>
<a name="l00093"></a>00093 <span class="stringliteral">            m_rbc ~ right boundary condition.</span>
<a name="l00094"></a>00094 <span class="stringliteral">            m_rbop ~ right compensation for implicit solution</span>
<a name="l00095"></a>00095 <span class="stringliteral">            m_load ~ rhs of the system of equations.</span>
<a name="l00096"></a>00096 <span class="stringliteral">            m_ival ~ initial value</span>
<a name="l00097"></a>00097 <span class="stringliteral">            m_numstepes ~ number of time steps.</span>
<a name="l00098"></a>00098 <span class="stringliteral">            m_numstages ~ number of internal states in extrapolation.</span>
<a name="l00099"></a>00099 <span class="stringliteral">            m_ftime ~ time to expiry.</span>
<a name="l00100"></a>00100 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00101"></a>00101 
<a name="l00102"></a>00102         (self.m_xl, self.m_xr) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00103"></a>00103         (self.m_rbc, self.m_srbop) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00104"></a>00104         (self.m_lbc, self.m_slbop) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00105"></a>00105         (self.m_mlbop, self.m_mrbop) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00106"></a>00106         (self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ae45823e09aa79d3ea37b16859392ebe6">m_load</a> , self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#af3f8f5561b7c17aa001dee0aa56392bf">m_ival</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00107"></a>00107 
<a name="l00108"></a>00108         (self.m_mass, self.m_stiff, self.m_jump) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00109"></a>00109 
<a name="l00110"></a>00110         (self.m_adaptive, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ade453e1905e535bfba9fbabb8e8d592b">m_method</a>) = (<span class="keyword">False</span>, <span class="keywordtype">None</span>)
<a name="l00111"></a>00111         (self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a31d66d09b3e829b4d0b3ddc6a20ccd11">m_dolog</a>, self.m_tol) = (<span class="keyword">False</span>, 1.e-16)
<a name="l00112"></a>00112 
<a name="l00113"></a>00113         (self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adcea8aebdd41cc16f72ef4b183ff0c40">m_numsteps</a>, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aea4ae21b5696276d876220775eeed2ca">m_numstates</a>, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa94fe3deb6a2a3a123ffefc4ce00a62d">m_ftime</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00114"></a>00114         (self.m_sfunc, self.m_quads, self.m_mesh) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00115"></a>00115 
<a name="l00116"></a>00116 
<a name="l00117"></a>00117     <span class="keyword">def </span>__euler(self, start, stop, nsteps):
<a name="l00118"></a>00118         <span class="stringliteral">&quot;&quot;&quot; Perform &#39;niter&#39; time steps and return. &quot;&quot;&quot;</span>
<a name="l00119"></a>00119 
<a name="l00120"></a>00120         deltat = (stop - start) / nsteps
<a name="l00121"></a>00121 
<a name="l00122"></a>00122         nsmat = self.m_mass.todense() + deltat * self.m_jump <span class="comment"># dense matrix</span>
<a name="l00123"></a>00123         smat = self.m_mass - deltat * self.m_stiff <span class="comment"># sparse matrix</span>
<a name="l00124"></a>00124 
<a name="l00125"></a>00125         tmp = self.m_ival.copy()
<a name="l00126"></a>00126         lbc_prev = self.m_lbc(self.m_xl, 0)
<a name="l00127"></a>00127         rbc_prev = self.m_rbc(self.m_xr, 0)
<a name="l00128"></a>00128 
<a name="l00129"></a>00129         (slbop, srbop) = (deltat * self.m_slbop, deltat * self.m_srbop)
<a name="l00130"></a>00130 
<a name="l00131"></a>00131         <span class="keywordflow">for</span> i <span class="keywordflow">in</span> range(0, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adcea8aebdd41cc16f72ef4b183ff0c40">m_numsteps</a>):
<a name="l00132"></a>00132             <span class="comment"># Fwd</span>
<a name="l00133"></a>00133 
<a name="l00134"></a>00134             time_k = deltat * (i + 1)
<a name="l00135"></a>00135             tmp = nsmat * tmp + deltat * self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a2fa6298df1be1d18c9d175ef70a54b7a">__inner_load</a>(time_k)
<a name="l00136"></a>00136 
<a name="l00137"></a>00137             <span class="comment"># Boundary contribution.</span>
<a name="l00138"></a>00138             lbc_current = self.m_lbc(self.m_xl, time_k)
<a name="l00139"></a>00139             rbc_current = self.m_rbc(self.m_xr, time_k)
<a name="l00140"></a>00140 
<a name="l00141"></a>00141             tmp += ((lbc_prev - lbc_current) * self.m_mlbop + \
<a name="l00142"></a>00142                     (rbc_prev - rbc_current) * self.m_mrbop)
<a name="l00143"></a>00143 
<a name="l00144"></a>00144             tmp += lbc_current * slbop + rbc_current * srbop
<a name="l00145"></a>00145 
<a name="l00146"></a>00146             lbc_prev = lbc_current
<a name="l00147"></a>00147             rbc_prev = rbc_current
<a name="l00148"></a>00148 
<a name="l00149"></a>00149             <span class="comment"># Implicit</span>
<a name="l00150"></a>00150 
<a name="l00151"></a>00151             tmp = spsolve(smat, tmp).reshape(self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#af3f8f5561b7c17aa001dee0aa56392bf">m_ival</a>.shape)
<a name="l00152"></a>00152 
<a name="l00153"></a>00153         <span class="keywordflow">return</span> tmp
<a name="l00154"></a>00154 
<a name="l00155"></a>00155     <span class="keyword">def </span>__inner_load(self, time):
<a name="l00156"></a>00156         <span class="stringliteral">&quot;&quot;&quot; proyect load in finite element space at time t. &quot;&quot;&quot;</span>
<a name="l00157"></a>00157 
<a name="l00158"></a>00158         <span class="keywordflow">if</span> self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ae45823e09aa79d3ea37b16859392ebe6">m_load</a> <span class="keywordflow">is</span> <span class="keywordtype">None</span>:
<a name="l00159"></a>00159             cload = zeros(self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#af3f8f5561b7c17aa001dee0aa56392bf">m_ival</a>.shape)
<a name="l00160"></a>00160 
<a name="l00161"></a>00161         tmp = oned_inner(self.m_sfunc, self.m_quads, self.m_mesh,
<a name="l00162"></a>00162                 self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ae45823e09aa79d3ea37b16859392ebe6">m_load</a>, time)
<a name="l00163"></a>00163 
<a name="l00164"></a>00164         <span class="keywordflow">return</span> tmp[1: -1]
<a name="l00165"></a>00165 
<a name="l00166"></a>00166 
<a name="l00167"></a>00167     <span class="keyword">def </span>__midpoint(self, start, stop, nsteps):
<a name="l00168"></a>00168         <span class="stringliteral">&quot;&quot;&quot; Implements the algorithm on page 318 of the paper. &quot;&quot;&quot;</span>
<a name="l00169"></a>00169 
<a name="l00170"></a>00170         deltat = (stop - start) / nsteps
<a name="l00171"></a>00171         ival0 = self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ac8cda79bc8ce7f019f6cf706842b7a74">__euler</a>(0, deltat, 1)
<a name="l00172"></a>00172 
<a name="l00173"></a>00173         smat = self.m_mass + deltat * self.m_stiff
<a name="l00174"></a>00174         nsmat = self.m_mass - deltat * self.m_jump
<a name="l00175"></a>00175         twojump = 2. * deltat * self.m_jump
<a name="l00176"></a>00176         twoload = 2. * deltat * self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ae45823e09aa79d3ea37b16859392ebe6">m_load</a>
<a name="l00177"></a>00177 
<a name="l00178"></a>00178         ival1 = self.m_ival.copy()
<a name="l00179"></a>00179         <span class="keywordflow">for</span> i <span class="keywordflow">in</span> range(1, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adcea8aebdd41cc16f72ef4b183ff0c40">m_numsteps</a>):
<a name="l00180"></a>00180 
<a name="l00181"></a>00181             <span class="comment"># Fwd</span>
<a name="l00182"></a>00182 
<a name="l00183"></a>00183             tmp = nsmat * ival0 + twojump * ival1 - twoload
<a name="l00184"></a>00184 
<a name="l00185"></a>00185             <span class="comment"># Boundary contribution.</span>
<a name="l00186"></a>00186 
<a name="l00187"></a>00187             time_k = deltat * (i + 1)
<a name="l00188"></a>00188             tmp = -(self.m_lbc(time_k) * self.m_mlbop + \
<a name="l00189"></a>00189                     self.m_rbc(time_k) * self.m_mrbop)
<a name="l00190"></a>00190 
<a name="l00191"></a>00191             <span class="comment"># Implicit</span>
<a name="l00192"></a>00192 
<a name="l00193"></a>00193             ival0 = ival1
<a name="l00194"></a>00194             ival1 = spsolve(smat, tmp)
<a name="l00195"></a>00195 
<a name="l00196"></a>00196         <span class="keywordflow">return</span> (ival0 + ival1) / 2.
<a name="l00197"></a>00197 
<a name="l00198"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa2acaae7188abf7af247dc7ea68ae2cc">00198</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa2acaae7188abf7af247dc7ea68ae2cc">set_boperators</a>(self, mlbop, mrbop, slbop, srbop):
<a name="l00199"></a>00199         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00200"></a>00200 <span class="stringliteral">        This operators will be applied by the time stepper</span>
<a name="l00201"></a>00201 <span class="stringliteral">        at each iteration. The time stepper will compute the</span>
<a name="l00202"></a>00202 <span class="stringliteral">        solution at time &#39;t&#39; at the points &#39;xl&#39; and &#39;xr&#39;,</span>
<a name="l00203"></a>00203 <span class="stringliteral">        modify them and compensate the fwd step.</span>
<a name="l00204"></a>00204 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00205"></a>00205 
<a name="l00206"></a>00206         (self.m_mlbop, self.m_mrbop, self.m_slbop, self.m_srbop) = (mlbop, mrbop, slbop, srbop)
<a name="l00207"></a>00207 
<a name="l00208"></a>00208 
<a name="l00209"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a5801ff40cd15997f4651861d35935e44">00209</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a5801ff40cd15997f4651861d35935e44">set_bcond</a>(self, lbc, rbc):
<a name="l00210"></a>00210         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00211"></a>00211 <span class="stringliteral">        Should be function of type (x, t).</span>
<a name="l00212"></a>00212 <span class="stringliteral">        they will be evaluated as needed by the time stepper.</span>
<a name="l00213"></a>00213 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00214"></a>00214 
<a name="l00215"></a>00215         (self.m_lbc, self.m_rbc) = (lbc, rbc)
<a name="l00216"></a>00216 
<a name="l00217"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adbea7d4ec795b49fe83e548c0d0c4cf0">00217</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adbea7d4ec795b49fe83e548c0d0c4cf0">set_dolog</a>(self, dolog):
<a name="l00218"></a>00218         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00219"></a>00219 <span class="stringliteral">        log progress ???</span>
<a name="l00220"></a>00220 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00221"></a>00221 
<a name="l00222"></a>00222         self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a31d66d09b3e829b4d0b3ddc6a20ccd11">m_dolog</a> = dolog
<a name="l00223"></a>00223 
<a name="l00224"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a724c9ac11f93da4af754a897e403a783">00224</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a724c9ac11f93da4af754a897e403a783">set_ival</a>(self, ival):
<a name="l00225"></a>00225         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00226"></a>00226 <span class="stringliteral">        Initial value projected in the finite element space.</span>
<a name="l00227"></a>00227 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00228"></a>00228         self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#af3f8f5561b7c17aa001dee0aa56392bf">m_ival</a> = ival
<a name="l00229"></a>00229 
<a name="l00230"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a0fd69687ad2f69a1abe0375dee34a277">00230</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a0fd69687ad2f69a1abe0375dee34a277">set_finite_elem_space</a>(self, sfunc, quads, mesh):
<a name="l00231"></a>00231         <span class="stringliteral">&quot;&quot;&quot; finite element space for time dependent load. &quot;&quot;&quot;</span>
<a name="l00232"></a>00232 
<a name="l00233"></a>00233         (self.m_sfunc, self.m_quads, self.m_mesh) = (sfunc, quads, mesh)
<a name="l00234"></a>00234 
<a name="l00235"></a>00235 
<a name="l00236"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a91166ac4075dd8c71c32a3237be42699">00236</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a91166ac4075dd8c71c32a3237be42699">set_load</a>(self, load):
<a name="l00237"></a>00237         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00238"></a>00238 <span class="stringliteral">        Accounts for modifying the initial value. Load is assumed to be</span>
<a name="l00239"></a>00239 <span class="stringliteral">        constant, time varying can be implemented too.</span>
<a name="l00240"></a>00240 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00241"></a>00241 
<a name="l00242"></a>00242         self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ae45823e09aa79d3ea37b16859392ebe6">m_load</a> = load
<a name="l00243"></a>00243 
<a name="l00244"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a38a8668da137bf7c5bd9f8e4255503f5">00244</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a38a8668da137bf7c5bd9f8e4255503f5">set_method</a>(self, method):
<a name="l00245"></a>00245         <span class="stringliteral">&quot;&quot;&quot; time stepping method. &quot;&quot;&quot;</span>
<a name="l00246"></a>00246 
<a name="l00247"></a>00247         <span class="keyword">assert</span> method <span class="keywordflow">in</span> [<span class="stringliteral">&#39;euler&#39;</span>, <span class="stringliteral">&#39;midpoint&#39;</span>, <span class="stringliteral">&#39;extrapolation&#39;</span>]
<a name="l00248"></a>00248         self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ade453e1905e535bfba9fbabb8e8d592b">m_method</a> = method
<a name="l00249"></a>00249 
<a name="l00250"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a86d514e8b761e7eb058762bd2210c8d7">00250</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a86d514e8b761e7eb058762bd2210c8d7">set_moperators</a>(self, mass, stiff, jump):
<a name="l00251"></a>00251         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00252"></a>00252 <span class="stringliteral">        Three matrices are needed to perform the time steps:</span>
<a name="l00253"></a>00253 <span class="stringliteral">        mass matrix, pde ~ stiffnes, jump ~ Toeplitz type.</span>
<a name="l00254"></a>00254 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00255"></a>00255 
<a name="l00256"></a>00256         (self.m_mass, self.m_stiff, self.m_jump) = (mass, stiff, jump)
<a name="l00257"></a>00257 
<a name="l00258"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ad0290eb80578ddc87aa2ab01b5769749">00258</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ad0290eb80578ddc87aa2ab01b5769749">set_number_steps</a>(self, numsteps):
<a name="l00259"></a>00259         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00260"></a>00260 <span class="stringliteral">        Will be used for non adaptive schemes.</span>
<a name="l00261"></a>00261 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00262"></a>00262 
<a name="l00263"></a>00263         self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adcea8aebdd41cc16f72ef4b183ff0c40">m_numsteps</a> = numsteps
<a name="l00264"></a>00264 
<a name="l00265"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a9cbb4b1f58137d54fcf87cf428a572d2">00265</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a9cbb4b1f58137d54fcf87cf428a572d2">set_numextrap_stages</a>(self, numstages):
<a name="l00266"></a>00266         <span class="stringliteral">&quot;&quot;&quot;</span>
<a name="l00267"></a>00267 <span class="stringliteral">        This number will define the max number of intermediate stages</span>
<a name="l00268"></a>00268 <span class="stringliteral">        to go from step i to step i+1. Case the algorithm does not</span>
<a name="l00269"></a>00269 <span class="stringliteral">        reach the desired tolerance, it will adjust the step size</span>
<a name="l00270"></a>00270 <span class="stringliteral">        and repeat the process.</span>
<a name="l00271"></a>00271 <span class="stringliteral">        &quot;&quot;&quot;</span>
<a name="l00272"></a>00272 
<a name="l00273"></a>00273         self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aea4ae21b5696276d876220775eeed2ca">m_numstates</a> = numstages
<a name="l00274"></a>00274 
<a name="l00275"></a>00275 
<a name="l00276"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a23273322062288923b33707169998da5">00276</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a23273322062288923b33707169998da5">set_time2simulate</a>(self, ftime):
<a name="l00277"></a>00277         <span class="stringliteral">&quot;&quot;&quot; Termination time for simulation.  &quot;&quot;&quot;</span>
<a name="l00278"></a>00278 
<a name="l00279"></a>00279         self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa94fe3deb6a2a3a123ffefc4ce00a62d">m_ftime</a> = ftime
<a name="l00280"></a>00280 
<a name="l00281"></a>00281 
<a name="l00282"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a0725dafcb725f6b5689bc41edaf828b4">00282</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a0725dafcb725f6b5689bc41edaf828b4">set_xlxr</a>(self, xleft, xright):
<a name="l00283"></a>00283         <span class="stringliteral">&quot;&quot;&quot; Evaluate left and right boundary conditions here. &quot;&quot;&quot;</span>
<a name="l00284"></a>00284 
<a name="l00285"></a>00285         (self.m_xl, self.m_xr) = (xleft, xright)
<a name="l00286"></a>00286 
<a name="l00287"></a>00287 
<a name="l00288"></a><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ac5e09504fe33085c02d90cc625254e1f">00288</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ac5e09504fe33085c02d90cc625254e1f">step</a>(self):
<a name="l00289"></a>00289         <span class="stringliteral">&quot;&quot;&quot; Stiffness will be solve implicitly, non-stiffness is explicit. &quot;&quot;&quot;</span>
<a name="l00290"></a>00290 
<a name="l00291"></a>00291         <span class="keyword">assert</span> 0 &lt; self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa94fe3deb6a2a3a123ffefc4ce00a62d">m_ftime</a> <span class="keywordflow">and</span> 0 &lt; self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adcea8aebdd41cc16f72ef4b183ff0c40">m_numsteps</a>
<a name="l00292"></a>00292         <span class="keyword">assert</span> self.m_slbop.shape == self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#af3f8f5561b7c17aa001dee0aa56392bf">m_ival</a>.shape
<a name="l00293"></a>00293         <span class="keyword">assert</span> self.m_mlbop.shape == self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#af3f8f5561b7c17aa001dee0aa56392bf">m_ival</a>.shape
<a name="l00294"></a>00294         <span class="keyword">assert</span> self.m_mrbop.shape == self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#af3f8f5561b7c17aa001dee0aa56392bf">m_ival</a>.shape
<a name="l00295"></a>00295         <span class="keyword">assert</span> self.m_srbop.shape == self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#af3f8f5561b7c17aa001dee0aa56392bf">m_ival</a>.shape
<a name="l00296"></a>00296 
<a name="l00297"></a>00297         <span class="keyword">assert</span> self.m_mesh <span class="keywordflow">is</span> <span class="keywordflow">not</span> <span class="keywordtype">None</span>
<a name="l00298"></a>00298         <span class="keyword">assert</span> self.m_sfunc <span class="keywordflow">is</span> <span class="keywordflow">not</span> <span class="keywordtype">None</span>
<a name="l00299"></a>00299         <span class="keyword">assert</span> self.m_quads <span class="keywordflow">is</span> <span class="keywordflow">not</span> <span class="keywordtype">None</span>
<a name="l00300"></a>00300 
<a name="l00301"></a>00301 
<a name="l00302"></a>00302         <span class="comment"># This iteration can be done more efficiently, the explicit</span>
<a name="l00303"></a>00303         <span class="comment"># step can be sped up because M is diagonal and jump is Toeplitz.</span>
<a name="l00304"></a>00304         <span class="comment"># Note that smat is sparse and nsmat is diagonal + Toeplitz.</span>
<a name="l00305"></a>00305 
<a name="l00306"></a>00306         <span class="keywordflow">if</span> self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ade453e1905e535bfba9fbabb8e8d592b">m_method</a> <span class="keywordflow">is</span> <span class="keywordtype">None</span>:
<a name="l00307"></a>00307             <span class="keywordflow">raise</span> ValueError, <span class="stringliteral">&#39;set the time sttepping method.&#39;</span>
<a name="l00308"></a>00308 
<a name="l00309"></a>00309         <span class="keywordflow">if</span> <span class="stringliteral">&#39;euler&#39;</span> == self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ade453e1905e535bfba9fbabb8e8d592b">m_method</a>:
<a name="l00310"></a>00310             psolu = self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ac8cda79bc8ce7f019f6cf706842b7a74">__euler</a>(0, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa94fe3deb6a2a3a123ffefc4ce00a62d">m_ftime</a>, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adcea8aebdd41cc16f72ef4b183ff0c40">m_numsteps</a>)
<a name="l00311"></a>00311 
<a name="l00312"></a>00312         <span class="keywordflow">if</span> <span class="stringliteral">&#39;midpoint&#39;</span> == self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#ade453e1905e535bfba9fbabb8e8d592b">m_method</a>:
<a name="l00313"></a>00313             psolu = self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#a30f7e43889c719026677a8a6aeab066e">__midpoint</a>(0, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa94fe3deb6a2a3a123ffefc4ce00a62d">m_ftime</a>, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#adcea8aebdd41cc16f72ef4b183ff0c40">m_numsteps</a>)
<a name="l00314"></a>00314 
<a name="l00315"></a>00315         solu = zeros((psolu.size + 2, 1), <span class="stringliteral">&#39;float64&#39;</span>)
<a name="l00316"></a>00316         solu[1: -1] = psolu
<a name="l00317"></a>00317         solu[0] = self.m_lbc(self.m_xl, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa94fe3deb6a2a3a123ffefc4ce00a62d">m_ftime</a>)
<a name="l00318"></a>00318         solu[-1] = self.m_rbc(self.m_xr, self.<a class="code" href="classsolvers_1_1IMEXTimeStepper_1_1IMEXTimeStepper.html#aa94fe3deb6a2a3a123ffefc4ce00a62d">m_ftime</a>)
<a name="l00319"></a>00319         <span class="keywordflow">return</span> solu
<a name="l00320"></a>00320 
<a name="l00321"></a>00321 
</pre></div></div>
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